Scales and chord formulas
Building chords relies on 2 main factors:
- Knowledge of Scales: this gives us the foundation of notes for building each chord.
- Knowledge of Chord Formulas: this give us a formula to apply to any given scale and construct each chord by substituting the notes of the scale into the formula.
Just to add a little spice to our knowledge of scales we have included the following table concerning Scale Degrees which defines each note in a scale in several different ways. It is good practice to become familiar with all of these terms, as you will see them used often... very handy to know.
|Interval||First||Second||maj or min Third||Fourth||Fifth||maj or min Sixth||maj or min Seventh|
A Scale Degree is the name given to a particular note in a scale in relation to the tonic (first note), which is the most important note in a scale. They are defined by Roman Numerals, names, intervals, or notes of the scale. In the following table, we will refer to each note as numbered notes of the scale, i.e., 1st, 2nd, 3rd, etc. If we were to include the 8th note of the scale it is referred to as the Octave (upper octave) or Super Tonic.If we think of the Tonic as the tonal center of a scale
- Supertonic and Subtonic are each one whole step above and below the Tonic
- Mediant and Submediant are each a third above and below the Tonic
- Dominant and Subdominant are each a fifth above and below the Tonic
- Please Note:
Subtonic is used when the interval between it and the tonic in the upper octave is a whole step, eg., 7 chord
Leading Tone is used when the interval between it and the tonic in the upper octave is a half-step, e.g., maj7 chord
1. Major Scales
When determining any type of chord, we need to know the major scale relating to each respective chord, e.g., if we need to calculate any type of C chord whether it be C Major, C minor, Cdim etc., we need to know the notes in a C Major Scale. The same applies to all other chords.
Building Chords - Observations from the table above:
- The major scales in lighter colors are not commonly used i.e., we would most likely use the B♭ Major Scale rather than the A# Major Scale; C# instead of D♭; E♭ instead of D#; F# instead of G♭, and A♭ instead of G#.
- x is another symbol for double sharp or ##
- We haven't included the 8th note of the scale, as it is the same as the first note or Tonic, except it is 1 Octave higher. If we were referring to the name of the Scale Degree, it would be called Octave... it is also referred to as Tonic or Upper Tonic.
- The C Major Scale has no sharps or flats.
2. Chord Formulas
There are a multitude of chord types and extensions. Each type of chord has a formula which tells us which notes of the major scale make up each chord.
When building chords, the first letter of the chord tells us the major scale we will apply the formula to, e.g., a Dm chord will use the D major scale as the basis to which a minor chord formula is applied; a Cmaj7 will use a C major scale as the basis to which a maj7 chord formula is applied; a Bm7 will use a B major scale as the basis to which a m7 chord formula is applied, etc. We include some of the most common types.
ExamplesOnce you know your major scales, and know the formula for each chord type, you will be able to work out any chord on the fly. Next time you're at band practice and someone asks you to play a certain chord and you have no idea what it is, e.g., D half-diminished 7th, you simply use the chord formula for a half-diminished 7th chord (1 - ♭3 - ♭5 - ♭7) on the D Major scale (D - E - F# - G - A - B - C#), and substitute the specific notes of the scale with its alterations (♭) into your formula, and there you have it... D - F - A♭ - C. If you find this example a little difficult, we will look at a few more examples.
Example 1: Building a Cm chord
- Write down the notes of the C major scale... C - D - E - F - G - A - B
- Write down the formula for a minor chord... 1 - ♭3 - 5
- Substitute the notes from the scale into the formula... C - E♭- G
Example 2: Building a Gm7 chord
- Write down the notes of the G major scale... G - A - B - C - D - E - F#
- Write down the formula for a minor 7th chord... 1 - ♭3 - 5 - ♭7
- Substitute the notes from the scale into the formula... G - B♭ - D - F
Example 1: Building an F diminished 7th chord (Fdim7, Fо7)
- Write down the notes of the F major scale... F - G - A - B♭ - C - D - E
- Write down the formula for a dim7 chord... 1 - ♭3 - ♭5 - ♭♭7
- Substitute the notes from the scale into the formula... F - A♭- C♭(B) - E♭♭(D)
This last example is a little more difficult to understand. Remember we are working with a diatonic scale where every note in the scale must have a different name. We write C♭ because we are referring to the 5th note of the F major scale which is C. We write it as C♭, but in actual fact it is really B. The same applies to the E♭♭... we write it like this because we are referring to the 7th note of the F major scale which is E, but in actual fact it is really D... the actual notes are seen in brackets in the example above.
If you know your Scales along with the notes on the guitar fretboard, building chords will be a breeze. It's amazing what you will achieve once you become familiar with this, and as far as chord formulas are concerned, you may have to freshen up on some of the harder ones from time to time, but the more you use them the easier they become.